“In fact within the game of Magic there are only interactions. There is no such thing as a ‘Magic card’. This is a difficult ontological reality for many Magic players to accept.”Stephen Menendian 29.Dec.2008

I remember now and will in all likelihood always remember where I was when I read that sentence. A loaded backpack hung slack from my right shoulder the bulge of a tennis shoe issuing uneven fissures in the black canvas topography. A carpet of clouds gray and cerebral intercepted all sunlight that would have gushed through the enormous painfully-clear window to my left. I tapped my foot and waited for a window to load. Standing beside me a tall and jowl-faced Asian man with a comb-over that somehow worked checked his watch and stared waiting. The scene: Terminal E14 Seoul-Incheon International Airport 4:15pm. A free public-use internet kiosk with one instruction: FREE 15 MINUTES MAXIMUM AS MUCH.

The page loaded I saw the words “Richard Garfield” in the body text and I set about digesting as much as possible of this end-of-year tour-de-force before my time expired.

There is no such thing as a Magic card.

Stephen was right of course in that a card is at its heart only a series of instructions actions and potentials that interface with other declared sequences of instructions actions and potentials to create a game. That in and of itself is a remarkable thing to conceptualize given how frequently we take the ‘cards’ themselves for granted. But as the little timer ticked down in the bottom-right-hand-corner of my screen as the chill air settled on my exposed cheeks and even inside I could almost see the cone of breath exit from my lips as I exhaled a thought bubbled up into the recesses of my brain and set off a veritable firestorm of flashing EMERGENCY! caution-lights:

“If there are no cards then there can be no card advantage.”

The clock hits zero the exasperated man shuffles folders around in his briefcase the clouds part just a little and permit a thin track of sunlight to paint the faintest hint of color on my cheekbones. But the monitor says “thank you!” and shuts off Windows ding-dongs its goodbyes passengers queue to intercom instructions and before I know it I’m dozing off in Seat 1C of Singapore Airlines Flight 550 en route to Kuala Lumpur the thought mulling and turning over like an insomniac in the dead of night.

Because the rabbit hole is deep and it goes and goes and goes and the little white eyes inside dart rapidly as they welcome their new visitor shrill sounds like sheathed daggers and as you crawl in further and further and further and the sunlight from above pinholes into impotence and the tunnel slopes and becomes something horizontal and you can see finally - as all this happens suddenly a creature you barely recognize takes you by the hand points to the fleeting shadows and commands: explore.

…

It doesn’t fall entirely outside the realm of possibility that I might in fact propose marriage to an Esper Battlemage. Okay sure: the made-of-metal thing requires some working-around and a search for “Mage of Battle” on Craigslist doesn’t exactly turn up a host of employment opportunities leaving me to foot the bill(s). But let me cast that sweetheart in a triple-Shards draft or heaven forbid recur it with a Sanctum Gargoyle after it’s already baited an Agony Warp or Resounding Thunder and it’s going to be kind of hard for me to lose.

Sometimes sure she sits there and takes out a Goblin Deathraiders and a Hissing Iguanar or an Akrasan Squire and a Sighted-Caste Sorcerer and you get yourself a good ol’ straight two-for-zero. But even if she’s not killing anything attacking becomes something of a nightmare for them. Things that would normally trade simply die and things that would normally smash right through start to fall in battle to your scrawny little weaklings. But even if they want to race you’re frequently halving their damage output should you opt not to block and negating a good chunk of certain lifelinked bombs like Rhox War Monk or Windwright Mage. In short the girl is a house.

But how do you quantify what’s happening there?

On one level of course it’s not exactly necessary to have a model that demonstrates why it’s frequently a huge beating to put cards on the table that are themselves huge beatings. We all kind of know that they are. But time and again certain repeatable effects from Rishadan Port to Skullclamp to Umezawa’s Jitte to Sword of Fire and Ice to Sensei’s Divining Top to Troubled Healer and Sparksmith and Timberwatch Elf and Silvergill Douser in Limited come to dominate formats. Many like Kabuto Moth and Saltfield Recluse and the aforementioned Skullclamp are initially undervalued. Some like Jund and Esper Battlemage and Vithian Stinger right now rise to the top but still aren’t valued nearly as highly as they ought to be. And if you ask me why that is it’s because we don’t really possess a good model for understanding exactly how brutal they can be.

What I propose and hope to outline in this article is a theory called Interaction Advantage. It aims to reconcile the competing existing concepts of Card Advantage and Card Quality with one another in a coherent fashion while incorporating the reality that certain effects have an impact on the board that far exceeds the expected interaction value of your average ‘card’ but aren’t easily measured by the other ‘cards’ they destroy negate or generate.

The thesis is this: the value of a given action can be measured by the number of favorable interactions it makes fungible relative to a theoretical maximum number of interactions of which your deck is capable or the number of an opponent’s favorable interactions it correspondingly negates.

That’s quite a mouthful so I’ll summarize: You want the maximize the impact of what you’re doing and minimize the impact of what your opponent is doing and you achieve that by interfacing with the opponent in favorable (to you) ways.

There are parallels of course to traditional card-advantage theory: when you draw cards you ‘enable options;’ when you kill your opponent’s guys or make him discard cards you take his options away. When you play a 5/5 to your opponent’s 3/3 you gain ‘virtual card advantage’ and initiative because barring another favorable-interaction-enabling card like a removal spell his ‘creature’ (which remember isn’t a ‘card’ but instead a mechanism that creates the interactions of dealing three damage to an opponent dealing three damage to a creature of your opponent’s choice being the target of one of your pump spells being the target of one of the opponent’s removal spells) loses all of its potential positive interactions until something changes. When you play Moat you remove an axis of interaction that all of your opponent’s non-flying creatures possess. And so on. The difference is that with this theory you don’t have to come up with a multitude of separate terms for concepts that are really trying to express the same thing—and crucially require assessments of “quality” without any hint beyond the subjective about what that ‘quality’ really means.

Finally: I mention “relative to your deck’s maximum potential interaction” because there are some decks that try as hard as they can not to be interactive meaning that they only interact with their opponent along a single very narrow axis (e.g. Brain Freeze You You’re Dead). My Shandalar deck for example is:

Its interactive potential is very very small ultimately: all of its cards enable it only to cast larger and larger Drain Lifes and point them at either creatures or the heads of particular opponents. But you can still approach the deck from an Interaction Advantage perspective because you’re aiming to try to maximize the potential for that one favorable interaction as much as possible and to avoid interference with that interaction as much as you can (usually by killing the opponent on the first turn).

I’m going to provide an example some of the situations that this system of thought resolves situations that have cropped up now and again in discussions of Magic theory. I hope to ignite further discussion in the forums. But some of the topics I’m going to cover are:

- What the operative difference is between a 0/1 Kobold Token and a 3/3 Beast token and whether one is “card advantage” while the other isn’t and whether that difference means anything;
- Why Esper Battlemage (and things like it) are so insane and should be valued highly;
- How to evaluate effects like Looting Pondering and Brainstorming and why it has always felt awkward to view them as ‘neutral’ in the existing card-advantage schema and why “Card Selection” doesn’t really cover it either;
- Why as the game goes longer and longer a card like Fathom Trawl becomes better than a card like Tidings;
- What Maze of Ith / Kor Haven / Icy Manipulator are actually doing;
- Why taking a mulligan in a format like Booster Draft frequently correlates more with a loss than in a format like Extended or at least why so many Extended/Legacy/Vintage decks are capable of winning within a format despite a high percentage of necessary mulligans

…

Kobold Oh So Bold

Oh tokens. From about as far back as we could create them - maybe not The Hive sure but certainly by the time Kjeldoran Outpost reared its head - the debate has raged about whether or not a token is a card. There are some who maintain that because tokens are not physical Magic cards then we should not apply the ‘card advantage’ metric to them in the first place because it complicates the model beyond its utility. Others with Adrian Sullivan being one of the most notable maintain that a Kobold Token a Soldier Token a Beast Token and a Marit Lage token are all cards but are cards which have different values and need to be treated as such. Finally still others argue that because a Kobold Token has an average value much lower than an average card in a given deck while a Beast Token (in Limited anyway) has a value equal to or higher than the average card in a given deck the Kobold does not count as a card while the Beast definitely does.

We should understand by now that because nothing is a card the first schema doesn’t really apply or at the very least becomes obsolete once you take that factor into account. But both the second and third have their merits. From a classical perspective it doesn’t really matter whether when you draw cards what the cards do. If I cast Concentrate and I draw three Kobolds of Kher Keep I still drew three cards. This is one of the reasons I love the Time Spiral land Kher Keep so much; it’s one of the easiest low-investment ways for a Red deck to gain some form of ‘card advantage.’ At the same time we have to recognize that we’re leaving some very vital variables out if we view the difference between 3/3 Beasts and 0/1 Kobolds as negligible.

From an Interaction Advantage perspective though the exact differences between Kobolds and Kelp and Saprolings and Faerie Rogues and Elephants and Beasts and Wurms and Marit-Lages become relatively easy to articulate. First of all they possess the same interactive possibilities as a physical card with the same properties except w/r/t their interactions with bounce spells and flicker effects. Since we know now that being a physical card isn’t a particularly important attribute we can quantify those differences with a relatively high degree of precision. We understand that losing the ability to attack eliminates an entire axis along which creatures are able to interact with other cards and with opponents at least halving the value of a Kobold relative to a Saproling absent pump or sacrifice effects to say nothing of what it does to its value relative to a 3/3 Beast. At the same time the need as mentioned before to analyze something’s interactive potential with the theoretical maximum of a given deck resurfaces. If in the case of something like Johnnie Walker Red all you want to do is point Beacons or Siege Gang Commander tokens or Chandra Nalaar pings at your opponent’s face and so the mode of interaction you care about is your token’s ability to block Chameleon Colossus then there is no operative difference between a Kobold and a Beast. Context in other words is everything.

…

What is Happening When You Get Smacked Around By Timberwatch Elf Or Whatever

Traditional card advantage doesn’t really provide a means of analyzing what happens when a Kabuto Moth is sitting there making it a nightmare to ever enter the combat phase. If it prevented you from playing spells - say if it were to prevent a Glacial Ray that’s in your hand from killing one of their creatures or if somehow all of your creatures can’t possibly attack without getting killed by their now-modified board - then virtual card advantage would have something to say about it. But I’m talking more about the degree to which your life is simply made more difficult by the presence of something like a Saltfield Recluse. You may not be totally shut down but something is definitely taking place and it’s important to understand what that is.

The operative variable about these types of repeatable effects is that they allow for their controller to pinpoint interaction at a place it is needed the most. That is while Esper Battlemage doesn’t quite say “B T: All of target opponent’s creatures get -1-1” it almost gets there because creatures are only meaningful insofar as they interact in certain ways. That is for an opponent’s creature to do anything it first needs to get into the red zone. Once this happens that creature is exposed to a myriad of possible interactions that it wasn’t before: it’s subject to the power variables of other creatures the wealth of spells that apply effects to attacking creatures the damage prevention ability of the Esper Battlemage and others. The net result of all these variables is that only a select few creatures are suitable for entering the red zone at all - and even once that determination is made the Battlemage can still target the creature upon which the use of its ability is most effective. So it is interacting positively not only with all of the creatures it forced not to attack but also (by contributing to the sum total of interactions) with the creatures that are still “relevant” by minimizing their value.

You can see then how such a creature would greatly contribute to its controller’s net interaction advantage.

…

Look Don’t Touch

Some effects allow you to “touch” - to actually draw X quantity of cards and put them into your hand. With others you “look” - you sit there and choose between one of X options put it into your hand and either discard another or shift others to the bottom of your library or rearrange the order in which they’re sitting there on top of your library or whatever. Now when you activate a Merfolk Looter you’re +1 then -1 for a total of zero on raw card advantage. Yet you’re still clearly ahead because if you sit there and do this for long enough it’s almost definitely going to win you the game as our experience and our willingness to first-pick the insane Looter il-Kor shows us. But what’s really happening here? In other words in a traditional card-advantage model there’s no real way to tell whether it’s better to go +1 once or to +1/-1 over a number of turns. Theories of interaction advantage on the other hand help you understand exactly what is going on.

When you Brainstorm as opposed to when you Ancestral Recall you still ultimately gain access to the same number of cards. That is when you cast the spell the very next action you take is likely to be the same (or is possible to be the same) regardless of whether you ACalled or BStormed because you choose from the same number of available options what the best thing to do with the rest of your turn is. The difference is the degree to which the interactions represented by the +2 cards that would be in your hand after an Ancestral are actually fungible or in other words whether they would affect the board after you’ve done the ‘best’ things available to you with the other X amount of cards in your hand. This is why in Vintage Brainstorm would occasionally be better than Ancestral particularly on the first turn because it creates the interaction of hiding one’s best spell from a discard effect while sacrificing nothing because the two cards atop the library are either irrelevant or not ready to be deployed.

Of course the overwhelming majority of the time Ancestral Recall is exponentially better because it’s incredibly easy in a format like Vintage to deploy resources to the table quickly and efficiently. In a format like Cube Draft or some hypothetical busted Limited format where it would be legal Ancestral Recall is again far superior but for a very different reason: it’s frequently important to win games of Cube or Limited by deploying a higher density of relevant threats. Yet Brainstorm at times can be almost as insane - especially when you’re “digging.” In these cases the interaction that matters is that you’re searching for one particular card that you need in your hand right away. Other times you’re sculpting a longer game and it doesn’t make a difference how quickly you deploy your options but rather that you have access to them within a particular time frame.

Brainstorm Ponder Impulse and their ilk are so good because they open up for you a ‘burst’ of potential interactions. The difference is that once you choose your option the other options go away at least temporarily. But this immediate creation of an incredibly diverse decision-tree gives you enormous interaction advantage even as your net distribution of cards remains equal.

Looting further complicates things. It either ups or affects neutrally your interaction advantage every single time it happens* because you receive a set of interactions (in the form of a card) whenever you do it and eliminate a set of interactions that you presume to be weaker. Eventually you’ve opened up broader and broader interaction-webs that should allow you to tailor your response or threat-deployment to whatever the opponent is doing. But what’s really insane about looting is when you take a card that has literally zero interaction potential - say a tenth land in a deck with only seven-mana spells and no net card-drawing - and exchange it for any card that does. In this case - and this is crucial to understand - what just took place is functionally indistinguishable from ‘actual’ card advantage. This is because and repeat it with me now a card is nothing but a set of interactions. When the potential for those interactions reaches zero a card is simply nothing.

…

Trawling In My Skin

Related to this last point is the functional difference between a card like Tidings and a card like Fathom Trawl and how this difference largely depends on the context within which the card operates (i.e. what deck it’s getting played in).

Put simply Tidings is going to be better when four random cards are going to have a higher sum total of interactive potentials than three guaranteed spells. An easy way to measure this is to look at the quantity of cards in a given deck whose interactive potential approaches zero because a high enough density of this kind of card allows Fathom Trawl to be strictly better than Tidings. Remember a card with an interactive potential of zero might as well not be a card.

The most common kinds of cards with an interactive potential of zero are redundant lands in decks without the ability to draw cards and creature removal spells. A Zoo deck without Dark Confidant or Pulse of the Forge can literally not do anything with Land Number Five after it empties its opening hand and neither can most Limited decks after land number eight or so. A Five-Color Control deck can literally not do anything with a Terror in a mirror that has clearly come down to who is going to Cruel Ultimatum first or even more drastically with a Wrath of God back when Turbo-Chant was a real deck. For these decks however lands almost always possess some kind of interactive potential because the second you draw a spell that might allow you to draw more than one card the need to deploy multiple threats in a turn plus the cost of the card-drawing spell itself arises. Frequently in fact the limiting factor will not be the number of favorable-interaction-creating cards to which the Five-Color Control player has access but rather the quantity of resources he has available to make those interactions happen.

So we can conclude from this then what is experientially obvious to all of us: when you’re in a topdeck war in Limited you would almost always rather have a Fathom Trawl because there’s a very realistic likelihood of your drawing two or more lands a very low likelihood of your drawing 4 spells and a very small possibility that being up four rather than three spells’ worth of interaction is going to be the operative difference between a win and a loss. Five-Color Control meanwhile would almost always rather play Tidings if it is going to play any of these cards at all because every single one of those four cards is going to have meaningful interactive potential and having adequate resources to deploy its powerful spells is a very important aspect of the deck’s strategy.

…

Ice Ice Baby

Icy Manipulator is one of the most powerful cards you can open in every single Limited format where it’s been legal and periodically makes a splash in Constructed from time to time as well. Maze of Ith and Kor Haven are both insanely frustrating cards to play against in Cube Draft and frequently spell “good game” for any deck that’s intending to play aggressive. Yet despite the fact that they can frequently neutralize (effectively) multiple threats in the same turn or facilitate possibilities on the counterattack that you couldn’t dream of otherwise from the perspective of traditional card advantage they are not actually doing anything. Let’s see though what’s happening through the lens of interaction advantage.

A creature’s chief means of interacting with anything as mentioned before is through attacking and blocking. Something like Maze of Ith by preventing that creature from ever attacking is obviously cutting off a line of its interactive potential. Kor Haven is going even further by not allowing that creature to block should it choose to attack in the first place and Icy Manipulator goes further in that it isn’t limited only to creatures. Each of these cards then generates progressively more interaction advantage until it is dealt with.

This is chiefly because tapping a creature reduces the vast majority of creatures’ interaction potentials to zero. In a deck with very few instants tapping a land during its controller’s upkeep also produces similar effects. And - for the third and last time - a card that can’t interact simply ceases to be a card.

…

Paris je t’aime

The recent sets of game-by-game play-by-play analyses by Richard Feldman GerryT and LSV were extremely useful for a variety of reasons. Getting insights into the minds of the game’s best is always valuable of course: seeing what goes through their heads when they make decisions what they’re trying to accomplish when they sideboard all the rest. But something else that was amazing to me was the sheer amount of time the decks took mulligans - and the amount of times they won in spite of it!

Looking at my DCI match history I have something like a 65% lifetime win percentage and I’d imagine that such a percentage holds true across a variety of different formats. But in thinking about it I’d say my game-win percentage after a mulligan in your average game of Sealed or Draft drops to around 40% and a mulligan to five puts me somewhere near 15-20%. In a format like Extended though I’d say I’m around 50% after a mulligan and maybe 30% after a mulligan to five. And with some decks even like Glass Cannon or Manaless Ichorid I’d say there’s almost no correlation between my taking a mulligan and my winning a match because you have to mulligan for value so often that most kept hands don’t vary that much or their variance is at least accounted for in deck construction.

My theory is that as formats expand the ability of individual cards to either create or eliminate potential interactions consequently expands so that while the value of an individual card exponentially increases the value of an individual card in the opening hand exponentially decreases. In fact it’s precisely because a single given card possesses so much more interactive potential that the sheer quantity of physical cards in the opening hand matters much less. What you need is simply a certain threshold of interactions and physical cards become far worse indicia of how close you are to an adequate number of interactions. Far more frequently you need to be doing very specific things with your opening hand in say Legacy and you need to be doing them quickly and so a seven-card hand with no clock Daze or Force of Will realistically has a lot less ‘access’ than many six-card hands. In Limited by contrast you’re simply playing lands for the first several turns you’re not doing pursuing some kind of ultra-narrow route where you simply cannot function without a Golgari Grave Troll or whatever and so the probability of taking a mulligan for value to accomplish a certain goal in particular decreases.

…

I strongly feel that the concept of interaction advantage could truly be revolutionary with regard to the way people approach not only how to play a given game but how to construct a deck how to draft how in theory even to design cards. Certainly I hope it will advance the dialogue into areas I haven’t had a chance to discuss or have only briefly touched on. Ultimately I hope it will allow us to hone our skills and understanding of the game to even greater levels of excellence and precision.

And maybe just maybe it’ll help both you and me to qualify for Honolulu.

Zac

* The notable exception being when you’re in the long game in Limited and you have two relevant threats in hand the risk being that you draw a third threat and are forced to discard a relevant card when it’s very possible that you’re going to need almost every threat in your deck to win.

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About Zac Hill

Zac Hill is a former member of Wizards of the Coast R&D. He worked there for three full years before deciding to move onto The Future Project as Chief Operating Officer in NYC. He also teaches, writes for the Huffington Post and The Believer, was a Luce Scholar in Malaysia, and authors poetry and short stories.